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Using the first few moments of the offspring distribution, one can obtain bounds on the ultimate probability of extinction (Courtois et al. 2006; Daley and Narayan 1980).
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We show herein that the ultimate probabilities of the different classes of codon mutation are complicated, nonlinear functions of the Taq misincorporation probabilities.
This theory predicts that the ultimate fixation probability of a novel neutral mutation (which is initially present as a single copy) is equal to 1/(2 Ne), where Ne is the effective size of the population (Kimura 1983).
At the ultimate level, the probability to receive future help should be increased by preferably helping needy social partners for such discrimination mechanism to evolve.
ASTEROID strikes are the ultimate in low-probability, high-impact events.
Inevitably no matter how big the wins, however large the initial streak, the slow steamroller of probability guarantees ultimate failure.
A principal problem of insurance risk theory is to find the probability of ultimate ruin.
Rather surprisingly, under these assumptions the probability of ultimate ruin as a function of the initial fortune x is exactly the same as the stationary probability that the waiting time in the single-server queue with Poisson input exceeds x.
In a random-mating population with N diploid individuals, k = 2Nux, where u is the neutral mutation rate per gamete per unit time (time measured in the same units as for k) and x is the probability of ultimate fixation of a neutral mutant.
Then the probability of ultimate ruin from initial surplus u is defined as ψ ( u ) = P ( T < ∞ | U ( 0 ) = u ).
It has been argued, however, that in both cases the ultimate justification for these probability distributions must be in terms of statistical patterns that ensembles of actual subsystems within a typical individual universe exhibit (Bell 1987, page 129, Dürr et al. 1992).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com